Absolutely Abnormal Numbers

Summary: A normal number is one whose decimal expansion (or expansion to some base other than 10) contains all possible finite configurations of digits with roughly their expected frequencies. This paper considers numbers that are absolutely abnormal (i.e., not normal in any base greater than 1) and exhibits a simple construction of a specific irrational real number that has this property.

About the Author: (from The American Mathematical Monthly, Vol. 108, (2001)) Greg Martin grew up in Spring, Texas and attended Stanford University as an undergraduate, receiving his bachelor's degree in 1992. He completed his doctorate in analytic number theory at the University of Michigan in 1997, under the supervision of Trevor Wooley and Hugh Montgomery (and thus may be the only person to have two Salem Prize winners as advisors). He worked for a year at the Institute for Advanced Study until, fearing that his movements were becoming too predictable, he fled the country for a postdoctoral position at the University of Toronto. He supplements his mathematical interests with a passion for collegiate a cappella music.